Yes, that is an intonation issue and is common, though worse on some guitars than others. The discrepancy depends on quite a few things, but I believe string tension and action height are pretty big factors.
When you depress the string you add tension to it, which pulls it sharp, and the more tension there is in the string to begin with, the more you add by depressing it a given distance at a given point. The G string has the highest tension by quite some margin, IIRC, which makes the effect more noticable. You can reduce the discrepancy by using lower tension strings, or by tuning down a bit if you don't need to be a concert pitch. I don't think you can really compensate for it by tuning the open string a bit flat, because the effect is not constant up and down the fretboard, and anyway you are going to want to use the open string at some point.
The basic design of the guitar assumes that when you fret a string, the vibrating length that you are left with is equal to the distance from the fret to the saddle - but this ignores the fact that the string has to rise to get to the saddle (if you put the guitar on its back, the saddle is higher than the fret). This effect should be pretty well compensated for in any well-built guitar, but the compensation is never going to be perfect because the effect varies along the string. You can get guitars with wavy frets that compensate much better (each fret is individually compensated) but are still based on standard 12 tone equal temperament. Those things are a bit zany though, if you ask me.